A physical constraint mechanism independent of a reference and a power battery power estimation method

Abstract

The application discloses a physical constraint mechanism and a power battery power estimation method without reference dependence, and belongs to the technical field of battery power estimation. The application embeds an electrochemical mechanism kernel driven by a physical information neural network (PINN) on the basis of a second-order RC-ECM benchmark model, utilizes a light-weight partial differential equation (PDE) embedding and an electrochemical cross-border translation and voltage fusion layer, realizes nonlinear dynamic correction of end voltage prediction under low computing power constraint, and finally completes high-robustness SOC accurate estimation under a full-temperature zone (especially a low-temperature edge working condition) based on a closed-loop observer.

Description

Technical Field

[0001] This invention belongs to the field of battery power estimation technology, specifically involving a physical constraint mechanism and a power battery power estimation method that does not depend on intrinsic parameters. Background Technology

[0002] As the most critical core state indicator in BMS, the accuracy of battery state of charge (SOC) estimation directly determines the accurate prediction of vehicle range, the active defense against overcharging and over-discharging, and the maximization of battery power characteristics.

[0003] Currently, the mainstream online SOC estimation technology for automotive terminals mainly relies on the combination of equivalent circuit models (ECM, such as the Thevenin model or second-order RC model) and Kalman filters (KF, such as extended Kalman filter EKF or unscented Kalman filter UKF). ECM, due to its simple structure and low computational cost, has become the optimal solution in current vehicle engineering deployments. However, ECM essentially uses lumped-parameter resistors and capacitors to simulate complex electrochemical polarization, charge transfer, and diffusion behaviors. Due to the lack of mechanistic constraints from fundamental electrochemical theorems (such as Nernst equation and Fick's diffusion law), this model exhibits strong limitations under various operating conditions. Under normal temperature and standard calibration conditions, ECM can maintain relatively stable voltage tracking performance; however, when entering low-temperature (e.g., below 0°C), high-rate, or deep-charge / de-discharge conditions that are not fully calibrated, the electrochemical reaction kinetics inside the battery slow down, and the charge transfer impedance and diffusion impedance increase exponentially and nonlinearly. At this time, the lumped-parameter model of ECM is prone to overfitting failure, leading to severe distortion of the predicted terminal voltage.

[0004] On the other hand, the Kalman filter algorithm, as a time-domain iterative algorithm based on a "prediction-update" architecture, inherently suffers from a strong dependence on initial state values. In real-world vehicle scenarios, due to open-circuit voltage (OCV) drift after prolonged inactivity, sensor initial zero-point residuals, or complex low-temperature transient start-up conditions, the BMS system often cannot obtain absolutely accurate initial values ​​for SOC and terminal voltage. When the initial voltage prediction value provided by the ECM is biased, the gain matrix of the Kalman filter becomes distorted. Not only does it fail to correct the initial bias within a finite time, but it also causes model errors and sensor noise to couple with each other during time-series iterations, triggering a vicious cycle and incremental accumulation of observation errors. Ultimately, this results in severe step shifts or long drifts in the SOC prediction curve under dynamic conditions.

[0005] To improve the physical consistency of battery management systems, academia and industry have attempted to introduce pseudo-two-dimensional (P2D) electrochemical models based on electrochemical kinetics. However, from the perspective of actual engineering practices for vehicle OEMs, this approach faces two irreconcilable obstacles: (1) The opaque barrier of core material parameters: Battery cells are usually purchased from battery manufacturers as standard outsourced components. The main equipment manufacturers have no way of obtaining the underlying core physicochemical parameters such as the radius of positive and negative electrode active particles, reaction rate constant, and solid-liquid phase conductivity. Without these key inputs, it is very difficult to develop and calibrate a high-precision electrochemical model.

[0006] (2) The computing power bottleneck of the vehicle microcontroller: The P2D model involves a large number of spatiotemporally coupled partial differential equations (PDEs). Even after simplification, the matrix iteration operation required for its online solution far exceeds the microsecond computing power limit of mainstream automotive-grade BMS chips.

[0007] In recent years, with the explosion of artificial intelligence technology, purely data-driven methods (such as LSTM and GRU neural networks) have been attempted for direct SOC mapping. However, these opaque models completely ignore the energy conservation and electrochemical mechanisms inside the battery. Their predictions often exhibit "ghost jumps" that violate physical common sense or output SOC curves that violate monotonicity in the untrained low-temperature range. They lack the interpretability and determinism required for safety applications and are difficult to meet the extremely stringent safety verification standards of the automotive industry.

[0008] However, directly applying Physical Information Neural Networks (PINNs) to real-time vehicle state estimation remains challenging. High-precision PINNs, in order to fully capture solid-state diffusion PDEs and nonlinear overpotentials, typically employ deep and wide network architectures, resulting in significantly slower online inference speeds compared to simpler second-order RC-ECM baseline models. If a multi-timescale or asynchronous Kalman filtering fusion strategy is forcibly adopted at the vehicle end (i.e., updating physical corrections only when the slow layer is triggered, freezing previous time-stamp values ​​or performing linear interpolation when not triggered), the actual polarization voltage changes extremely rapidly under severe transient conditions such as heavy acceleration or dynamic high-frequency energy recovery. Asynchronous updates easily introduce significant mechanistic hysteresis errors. Furthermore, when the slow layer completes its calculation and suddenly injects a new correction, the fused voltage experiences a step-like non-physical jump, causing a sharp increase in the Kalman filter residuals and gain matrix oscillations, leading to serious risks of online assessment timeouts and state estimation jumps. Therefore, how to maintain high physical consistency while enabling the mechanistic neural network to have a microsecond-level, constant-time forward computation speed, and achieve synchronous, smooth, and continuous fusion with the ECM benchmark model, has become the core technical bottleneck for breaking through the mass production and deployment of low-computing-power automotive chips. Summary of the Invention

[0009] The purpose of this invention is to address the problems existing in the prior art and provide a highly physically consistent PINN terminal voltage correction and SOC composite estimation framework that does not rely on the internal microscopic physical parameters of the battery (vehicle manufacturer friendly). This invention bypasses complex microscopic mechanism parameter calibration by using a Physical Information Neural Network (PINN). Under the low computing power constraints of the onboard BMS, it utilizes physical constraint terms to achieve nonlinear dynamic correction of the ECM predicted terminal voltage. By eliminating the initial value interference and observation error accumulation of the KF algorithm, it achieves highly physically consistent and highly generalizable accurate SOC estimation of the battery under low temperature and edge operating conditions, while also considering the interpretability and ease of secondary development of the algorithm.

[0010] To achieve the above objectives, the present invention provides the following solution: a physical constraint mechanism and a power battery capacity estimation method without intrinsic parameter dependence, comprising the following steps: Step 1: Based on bench experiments, acquire battery external characteristic data under complex dynamic conditions and different temperature ranges to obtain a mechanism dataset; construct a second-order RC-ECM benchmark model based on the mechanism dataset, and obtain the benchmark macroscopic terminal voltage based on the second-order RC-ECM benchmark model. Step 2: Obtain the macroscopic predicted voltage residual based on the reference macroscopic terminal voltage and the actual measured voltage; Step 3: Construct a physical information neural network, and embed the solid-state diffusion partial differential equation and boundary conditions evolving with temperature in spherical coordinates as physical constraint terms into the loss function of the physical information neural network; take time, current, temperature, and state of charge as inputs, and the macroscopic predicted voltage residual as data supervision term to obtain the nonlinear electrochemical voltage dynamic correction quantity; Step 4: Using the physical information neural network as the teacher network and the nonlinear electrochemical voltage dynamic correction amount as the soft label, train an ultra-lightweight feedforward neural network. Step 5: Deploy the ultra-lightweight feedforward neural network in the vehicle battery management system and run it synchronously with the second-order RC-ECM benchmark model at the same frequency to continuously output the nonlinear electrochemical voltage dynamic correction value; input the nonlinear electrochemical voltage dynamic correction value into the measurement equation of Kalman filtering to obtain the battery state of charge estimate.

[0011] More preferably, in step 1, the state-space equations of a second-order RC-ECM reference model are established, and the state-space equations are discretized using the first-order forward Euler method to obtain the state transition equations. Based on the state transition equations, the reference macroscopic terminal voltage is obtained. ; in, ; ; In the formula, express The reference macroscopic terminal voltage at that moment; Indicates open-circuit voltage; express The virtual state of charge at any given moment is calculated by the ampere-hour integral; express k Current at any moment; Indicates the internal resistance of the ohm; Indicates charge transfer impedance; Indicates charge transfer capacitance; Indicates concentration polarization impedance; Indicates concentration polarization capacitance; , They represent k The polarization voltages of the two RC loops at any given time; Indicates the sampling period; , They represent k+ The polarization voltages of the two RC loops at time 1.

[0012] More preferably, the composite multi-objective total loss function of the physical information neural network includes: ; In the formula, Represents the total loss function for composite multi-objectives; Represents the loss function for data-driven terms; This represents the residual loss function of the physical partial differential control equations; Represents the boundary condition residual loss function; These are the weighting coefficients for the data-driven term loss function, the physical partial differential equation residual loss function, and the boundary condition residual loss function, respectively.

[0013] More preferably, the residual loss function of the physical partial differential equation includes: ; In the formula, This indicates the concentration of lithium ions in the solid phase inside the active particles; This represents the solid-phase diffusion coefficient, which is strongly coupled with the real-time operating temperature. Indicates the radial radius position of the microscopic particles; Indicates the runtime.

[0014] More preferably, in step 3, the physical information neural network takes time, current, temperature, and state of charge as inputs to obtain the concentration distribution state; by constructing an electrochemical cross-boundary translation and voltage fusion layer, the concentration of the outermost surface of the active particles is extracted from the concentration distribution state. and the average concentration inside the active particles Normalization was performed to obtain the surface stoichiometry. and average stoichiometry ;in The maximum saturated solid concentration is represented by the Butler-Volmer kinetic equation in the charge transfer process and the solid concentration polarization mechanism induced by the surface-to-average concentration difference, to obtain the dynamic correction amount of the nonlinear electrochemical voltage. : ; In the formula, Represents the ideal gas constant; Indicates the operating temperature of the battery surface; Denotes Faraday's constant; This represents the molar flux of the electrode surface pores that is linearly mapped to the real-time charge / discharge current. This represents the exchange current density, which depends on local temperature and surface concentration. This represents the corresponding electrode equilibrium potential function.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention injects physical mechanism constraints into the equivalent circuit model (ECM) through a physical information neural network. Under extremely cold temperatures (such as -10°C) or complex uncalibrated dynamic boundary conditions, the model can adaptively eliminate the distortion in terminal voltage prediction caused by the surge in electrochemical polarization nonlinearity, thus significantly reducing the terminal voltage tracking error.

[0016] Under the extremely stringent computing power constraints of automotive-grade computing chips, this invention shatters the inherent contradiction between computing power bottlenecks and timing oscillations through knowledge distillation technology. The refined ultra-compact ANN network is extremely lightweight, with forward computation time in the microsecond range and completely constant, exhibiting extremely high timing determinism, and can be perfectly embedded into the original high-frequency control loop of the BMS. Due to its synchronous operation with the ECM model, the output voltage correction curve is smooth and continuous, fundamentally eliminating the numerical oscillations of Kalman filters and SOC ghost jumps caused by sudden step changes in asynchronous fusion schemes. Under the premise of zero task timeout risks, it ensures the extreme robustness of dynamic safety power estimation throughout the entire vehicle lifecycle.

[0017] This invention avoids the massive spatiotemporal iterative solutions of partial differential equations, and the trained PINN model possesses end-to-end ultra-fast inference capabilities. It has extremely low memory footprint and minimal computational overhead, and can be perfectly compatible with and run on current mainstream automotive-grade low-computing-power BMS chips. Because it does not request any material parameters from battery manufacturers, it provides OEMs with extremely high freedom for secondary development, algorithm interpretability, and independent PHM control capabilities, making it highly valuable for industrial applications. Attached Figure Description

[0018] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A schematic diagram illustrating a physical constraint mechanism and power battery capacity estimation method without intrinsic parameter dependence provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the current curve under test conditions for heavy-duty commercial vehicles provided in an embodiment of the present invention; Figure 3 The diagram shows the battery terminal voltage prediction results of the conventional second-order EC-ECM under CHTC conditions provided in the embodiments of the present invention; wherein, (a) is a diagram showing the verification results of the second-order ECM predicted voltage under CHTC conditions; and (b) is a diagram showing the residual of the ECM predicted voltage. Figure 4 The following is a convergence graph of the loss function during PINN training provided in an embodiment of the present invention; Figure 5 A schematic diagram of the battery terminal voltage prediction effect of the second-order RC-ECM model incorporating ANN provided in the embodiment of the present invention; wherein, (a) is a schematic diagram of the battery terminal voltage prediction result; and (b) is a schematic diagram of the terminal voltage prediction error result. Figure 6 The diagram shows a comparison of the closed-loop SOC estimation results of the ANN+RC-ECM provided in the embodiments of the present invention; wherein, (a) is a schematic diagram of the SOC estimation results; and (b) is a schematic diagram of the voltage residual results. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0022] Example 1: like Figure 1As shown, this embodiment provides a physical constraint mechanism and power battery capacity estimation method without intrinsic parameter dependence. Based on a second-order RC-ECM benchmark model, this invention innovatively embeds an electrochemical mechanism kernel driven by a Physical Information Neural Network (PINN). Utilizing lightweight partial differential equation (PDE) embedding and an electrochemical cross-boundary translation and voltage fusion layer, it achieves nonlinear dynamic correction of the terminal voltage prediction under low computational constraints. Finally, based on a closed-loop observer, it completes highly robust and accurate SOC estimation across the entire temperature range (especially at the low-temperature edge conditions). Detailed implementation steps are as follows: Step 1: Based on bench experiments, obtain battery external characteristic data under complex dynamic conditions and different temperature ranges to obtain a mechanism dataset; construct a second-order RC-ECM benchmark model based on the mechanism dataset, and obtain the benchmark macroscopic terminal voltage based on the second-order RC-ECM benchmark model.

[0023] This step involves high-precision bench testing to obtain macroscopic external characteristic data of power batteries covering a wide temperature range and complex dynamic operating conditions, providing a data foundation for subsequent model identification and network training.

[0024] Specifically, the open-circuit voltage (OCV-SOC) curve is calibrated at room temperature: Under standard ambient temperature (e.g., 25°C), a slow charge-discharge experiment with a small current is conducted on the test cell to accurately extract the equilibrium potential corresponding to different states of charge (SOC) points, and to construct a battery open-circuit voltage mapping function. .

[0025] Perform variable-temperature hybrid pulse power characteristic (HPPC) testing: Place the battery in different temperature environmental chambers, especially in extremely cold low-temperature ranges (such as 0°C, -10°C, -20°C), and perform standardized HPPC pulse charge-discharge tests. By capturing the transient voltage step and response curves of pulse excitation, a core excitation signal is provided for the identification of equivalent circuit element parameters under different temperatures and charge states.

[0026] Multi-factor dynamic testing under various verification conditions: Standard vehicle driving conditions (such as CHTC, CLTC, DST, etc.) are introduced for continuous dynamic testing, recording high-frequency macroscopic time-domain signals that change over time, including current. Terminal voltage and battery surface operating temperature By utilizing the ampere-hour integration method combined with long-term static calibration, high-fidelity true state-of-charge labels are obtained. The final processing results in a multivariate hybrid mechanism dataset consisting of a training set, a validation set, and a test set.

[0027] To ensure extremely low computational overhead for the vehicle-mounted BMS, this embodiment uses a second-order RC equivalent circuit model as the basic external characteristic characterization tool.

[0028] Based on the HPPC test data obtained in the above steps at different temperatures and SOC nodes, the core lumped parameters in the second-order RC equivalent circuit model were identified offline using the nonlinear least squares method in the Python development environment. These parameters included the ohmic internal resistance. Charge transfer impedance Charge transfer capacitor Concentration polarization impedance and concentration polarization capacitor .

[0029] The state-space equations of a second-order RC-ECM baseline model are established and discretized using the first-order forward Euler method to facilitate online time-domain iteration. The discretized state transition equations and terminal voltage output equations are expressed as follows: ; ; ; In the formula, express The reference macroscopic terminal voltage at that moment; Indicates open-circuit voltage; express The virtual state of charge at any given moment is calculated by the ampere-hour integral; express k Current at any moment; , They represent k The polarization voltages of the two RC loops at any given time; Indicates the sampling period; , They represent k+ The polarization voltages of the two RC loops at time 1.

[0030] The five parameter matrices obtained from offline identification are encapsulated into […]. , A two-dimensional lookup table with [ ] as the base axis. During the operation of the onboard BMS, based on the estimated charge obtained from the integration of the current and real-time temperature, the ECM parameters are updated in real time through fast bilinear interpolation, and the reference macroscopic terminal voltage is calculated forward. .

[0031] Step 2: Obtain the macroscopic predicted voltage residual based on the reference macroscopic terminal voltage and the actual measured voltage. In this embodiment, the macroscopic predicted voltage residual is defined as the difference between the actual measured voltage and the reference macroscopic terminal voltage.

[0032] Step 3: Construct a physical information neural network, and embed the solid-state diffusion partial differential equation and boundary conditions evolving with temperature in spherical coordinates into the loss function of the physical information neural network as physical constraint terms; take time, current, temperature, and state of charge as inputs, and the macroscopic predicted voltage residual as data supervision term to obtain the nonlinear electrochemical voltage dynamic correction quantity.

[0033] To overcome the drawbacks of data-driven models, namely "lack of interpretability" and "prone to overfitting," this embodiment constructs a Physical Information Neural Network (PINN) rigidly constrained by the dual laws of matter conservation in electrochemical single-particle theory (SPM) and energy conservation in heat transfer. This model is used to eliminate the macroscopic predicted voltage residuals extracted in step 2 on the unseen internal microscopic spatiotemporal manifold.

[0034] The Physical Information Neural Network (PINN) constructed in this invention adopts a "macro-micro" multi-scale deep composite network architecture, which is a combination and integration of macro-feature networks and micro-mechanism networks. Specifically, the macro-scale fully connected network (FCNN) serves as the macro-scale representation layer of PINN. The input to this network is a macro-measurable feature vector [time, current, SOC, battery temperature], and through nonlinear forward mapping of multiple layers of fully connected neurons, it outputs the macro-scale terminal voltage residual. and macroscopic temperature The micro-mechanism network serves as the micro-electrochemical mechanism reconstruction layer of PINN. Based on the input features, this network collaboratively splices together one-dimensional radial spatial relative coordinates. ( Using the spatial independent variable as input, this study aims to leverage the powerful fitting ability of neural networks to independently predict the spatiotemporal distribution of the solid-phase lithium-ion concentration field inside microscopic active spherical particles. .

[0035] Specifically, to address the technical problem that traditional ECM models lack electrochemical microdynamic constraints under low-temperature conditions, leading to parameter extrapolation distortion, this embodiment embeds a solid-phase diffusion mechanism kernel in spherical coordinates into the physical information neural network.

[0036] Numericalization of Fick's Second Diffusion Law: Considering the lithium-ion insertion / extraction barriers within the positive / negative electrode active material particles, a solid-state diffusion partial differential equation (PDE) evolving with temperature in spherical coordinates is introduced. A data-driven backbone of a Physical Information Neural Network (PINN) is used to output or predict the lithium-ion concentration distribution within the particles. ,in, Indicates the radial radius position of the microscopic particles; Indicates the runtime.

[0037] Constructing Partial Differential Equation Residuals: To ensure that the physical information neural network strictly adheres to mass conservation and electrochemical physics mechanisms during training and inference, this embodiment proposes a physical partial differential equation residual loss function. Its specific mathematical expression is: ; In the formula, This indicates the concentration of lithium ions in the solid phase inside the active particles; This represents the solid-phase diffusion coefficient, which is strongly coupled with the real-time operating temperature, and its variation with temperature follows Arrhenius's law.

[0038] To ensure the physical uniqueness of the PDE boundary value, a boundary condition residual term is simultaneously introduced into the loss function. At the center of the active particle ( The solid concentration gradient is zero; at the surface of the active particles ( , (Represents the outer radius of the particles), and the molar flux of the electrode surface pores that is linearly mapped to the real-time charge-discharge current by the solid-phase concentration gradient caused by the macroscopic current. constraint: ; In the formula, This represents the Faraday constant.

[0039] By transforming the aforementioned boundary conditions into a mean squared error term and incorporating it into the network penalty, PINN is forced to output a microscopic concentration field distribution that perfectly conforms to physical consistency, even in the low-temperature "opaque" edge case where internal label data is lacking. Specifically, the boundary condition residual loss function... include: .

[0040] The composite multi-objective total loss function of a physical information neural network is: ; In the formula, This represents the composite multi-objective total loss function, used for global gradient backpropagation of the physical information neural network during the offline training phase; This represents the data-driven loss function, used for network-fused voltage prediction. Actual voltage measured in bench test The mean square error between them, adjust it with Figure 3 The alignment of the experimental voltage error is shown. This represents the boundary condition residual loss function, used to monitor the microparticles at the center ( ) and surface ( Does the concentration gradient strictly conform to flux constraints? These are the weighting coefficients for the data-driven term loss function, the physical partial differential equation residual loss function, and the boundary condition residual loss function, respectively.

[0041] This invention introduces a dynamic weight adjustment strategy to collaboratively optimize the network during training. The optimal weighting ratio effectively solves the problems of gradient hedging and numerical artifacts between loss functions of multiple tasks, ensuring the optimal convergence of network weights.

[0042] Since the solid concentration field in the microscopic mechanism space cannot be directly compared with the macroscopic electrical signals directly collected by the vehicle-mounted sensors, this embodiment constructs an electrochemical cross-border translation and voltage fusion layer to map microscopic physical quantities into macroscopic terminal voltage correction residuals.

[0043] First, surface concentration and state translation extraction are performed: the concentration of the outermost surface of the active particles is accurately extracted from the constructed PINN solid-phase concentration field. and the average concentration inside the active particles The surface stoichiometry, which characterizes the degree of embedding on the electrode surface, is obtained by normalizing it. and average stoichiometry ;in This represents the maximum saturated solid concentration.

[0044] Butler-Volmer inverse operation and voltage fusion: Utilizing the Butler-Volmer (BV) kinetic equation in the charge transfer process and the solid-phase concentration polarization mechanism induced by the surface-to-average concentration difference, a dynamic correction for nonlinear electrochemical voltage is obtained. The fusion calculation formula is as follows: ; In the formula, Represents the ideal gas constant; Indicates the operating temperature of the battery surface; This represents the molar flux of the electrode surface pores that is linearly mapped to the real-time charge / discharge current. This represents the exchange current density, which depends on local temperature and surface concentration. This represents the electrode equilibrium potential function.

[0045] The first term of the equation The nonlinear activation overpotential induced by the slower charge transfer rate at low temperatures was rigorously characterized; the second term This accurately captures the solid phase concentration overpotential caused by the obstruction of low-temperature diffusion and the distortion of the concentration gradient inside and outside the particle.

[0046] Finally, the mechanism correction amount obtained from the cross-border translation The reference macroscopic terminal voltage calculated by the second-order RC-ECM reference model in step 1 Nonlinear superposition and fusion are performed to output a final predicted terminal voltage with high physical consistency. .

[0047] Step 4: Using a physical information neural network as the teacher network and a nonlinear electrochemical voltage dynamic correction quantity as a soft label, an ultra-lightweight feedforward neural network is trained.

[0048] This step aims to solve the engineering challenges of slow inference speed of deep physical information neural networks, which cannot be directly matched with the high-frequency real-time control loop of vehicle BMS, and achieve the ultimate integration of computing power and accuracy through knowledge extraction.

[0049] During the offline training phase, the PINN architecture is built to be relatively deep and wide. Combined with the physical loss function and soft boundary constraints of the single-particle model (SPM), it thoroughly learns the complex solid-state diffusion partial differential equations and charge transfer nonlinear voltage residuals within the power battery under wide temperature ranges and extreme edge conditions. After the deep PINN network is trained offline, its large number of layers and matrix computations make it unsuitable for direct deployment in computationally strained automotive MCUs. This embodiment introduces knowledge distillation technology to dynamically correct the nonlinear electrochemical voltage output by the trained deep PINN network. This serves as a "soft label." It is used to train an ultra-compact, ultra-lightweight feedforward neural network (ANN). The ANN contains only 2-3 hidden layers, with each layer containing only 8-16 neurons. Through "knowledge transfer" from the large network to the small network, the ultra-compact ANN perfectly inherits the high-precision fitting capability of the large network for voltage residuals across all operating conditions, all within a very small footprint.

[0050] Step 5: Deploy the ultra-lightweight feedforward neural network in the vehicle battery management system and run it synchronously with the second-order RC-ECM benchmark model at the same frequency to continuously output the nonlinear electrochemical voltage dynamic correction value; input the nonlinear electrochemical voltage dynamic correction value into the measurement equation of Kalman filter to obtain the battery state of charge estimate.

[0051] The ultra-compact ANN obtained through offline distillation is hard-coded and deployed in an onboard BMS microcontroller (MCU). Due to the extremely small size of the network, its online inference essentially consists of only a few sets of simple matrix multiplication and addition operations on the order of microseconds, and the computation time of each step is completely constant, exhibiting extremely high timing determinism. Therefore, this ultra-lightweight ANN can fully keep up with the pace of a second-order RC-ECM, outputting high-frequency, synchronous, and continuous voltage dynamic correction at the same control frequency (e.g., 10Hz or 100Hz). By injecting this smooth, stepless corrected voltage into the measurement equation of the Kalman filter (KF) as a real-time, highly consistent observation benchmark for the closed-loop observer, not only is the dependence of the Kalman filter on the initial charge residual completely eliminated, but the non-physical numerical oscillations of the filter that are easily caused by asynchronous time-scale fusion are also eliminated. Finally, highly robust and accurate SOC estimation results are generated online.

[0052] Example 2: This embodiment provides a specific example to illustrate the method of the present invention. The implementation consists of five steps: ECM parameter calibration; RC-ECM prediction of heavy commercial vehicle test condition (CHTC) voltage; training the PINN model using the predicted voltage residuals; PINN knowledge distillation to form an ANN; and ANN-assisted ECM for online closed-loop SOC estimation.

[0053] (1) ECM parameter calibration.

[0054] A baseline for the pure electrical behavior of the battery under a standard temperature (25°C) condition was established. The core linear voltage drop and resistance-capacitance characteristics of the battery at different states of charge (SOC) throughout its entire life cycle were identified.

[0055] The lithium-ion battery was placed in a 25°C test chamber and fully charged using a standard constant current-constant voltage method, followed by a period of rest to eliminate concentration differences. A standard HPPC composite current pulse was then applied. Finally, the ohmic internal resistance was extracted based on the vertical voltage jump at the moment the pulse was cut off, using a nonlinear least squares fitting algorithm. Based on the voltage exponential relaxation exponential rebound tail, the first-order electrochemical polarization is decoupled and fitted ( ) and second-order concentration polarization ( The resistance and capacitance parameters are shown in Table 1.

[0056] Table 1 ; (2) RC-ECM predicts the voltage of heavy commercial vehicle test condition (CHTC).

[0057] Using a calibrated second-order RC-ECM baseline model, the battery terminal voltage under CHTC conditions (20°C) is predicted. The polarization distortion of the traditional room-temperature equivalent circuit model is quantified when facing dynamic, drastic temperature changes and high-frequency current surges in actual driving conditions. Through pure open-loop recursion, the difference between the room-temperature circuit prediction and the true value from the dynamic temperature experiment is calculated, thereby accurately identifying the nonlinear residuals of the external voltage caused by impeded microscopic solid-phase diffusion and thermodynamic deviations. This provides a target supervision label for the subsequent training of the PINN model.

[0058] Import standard CHTC dynamic driving conditions that include complex timing characteristics and high-power accelerated discharge behavior, such as... Figure 2 As shown. The algorithm is in Align with the initial state at all times, and then adjust the timing of the driving current. and temperature The voltage is injected into a calibrated 25°C second-order RC-ECM baseline model. In the full-sequence forward extrapolation, the State of Charge (SOC) is continuously recursively derived using pure open-loop ampere-hour integration, while the polarization capacitor voltage is derived through a hard extrapolation of state-space discretization equations. The basic open-loop predicted voltage is then rapidly output via table lookup mapping. Finally, the actual measured voltage of the battery platform obtained by the sensor will be used. With circuit model voltage Perform synchronization difference calculation to generate a macroscopic predicted voltage residual data series. : .

[0059] Figure 3 Based on the prediction results of traditional RC-ECM, the test conditions involved high-rate discharge at a temperature of 20°C, which deviates from the 25°C ambient temperature environment used for RC-ECM model parameter calibration. Therefore, the purely open-loop recursive second-order RC-ECM exhibits severe electrochemical and thermal conduction distortions. During the intense acceleration pulse segment and in the steep low-charge (<15% SOC) region, the terminal voltage experiences severe polarization shift, resulting in a typically large root mean square error (RMSE) of the total-sequence terminal voltage. Figure 3 Although the green error (mV) residual curve exposes the shortcomings of the traditional RC-ECM mechanism, it also shows the lithium-ion diffusion distortion characteristics caused by temperature differences, which becomes the key data for training the PINN model.

[0060] (3) Use the predicted voltage residual to train the PINN model.

[0061] The macroscopic fully connected network (FCNN) takes [time, current, SOC, battery temperature] as input and outputs the voltage residual after forward mapping. and temperature The microscopic mechanism network is then pieced together with 1D radial spatial relative coordinates. Output the solid-phase lithium-ion concentration field inside the spherical particle separately. A compound penalty term is introduced into the loss function design: the data terms are adjusted using the mean squared error (MSE). and Figure 3Alignment of error (mV); physical mechanism constraint terms are randomly assigned to virtual machine physical points within a two-dimensional spatiotemporal grid, and partial derivatives are extracted online using the automatic differentiation of the deep learning framework. These partial derivatives are then directly substituted into the partial differential equation of lumped parameter thermal equilibrium and the partial differential equation of Fick's second diffusion law of the SPM model to calculate the remainders. At the same time, rigid strong boundary conditions are added, such as flux of 0 at the center of the sphere (BC1) and surface concentration slope equal to macroscopic normalized current (BC2).

[0062] like Figure 4 As shown, the total loss function of the multi-objective network and the residual losses of each physical equation exhibit a perfect logarithmic downward slope with each training epoch. After training convergence, the network can not only align voltage deviations with extremely high precision, but also, due to the rigid constraint of the partial differential equations, spontaneously evolve a microscopic concentration profile field that satisfies mass conservation and physical diffusion laws within the completely invisible particles. .

[0063] (4) PINN knowledge distillation forms ANN.

[0064] By using knowledge distillation technology, the smooth physical manifold and diffusion mechanism mastered by PINN are dimensionally reduced and unidirectionally transferred to ANN, overcoming the problem that high-fidelity models cannot be deployed in real time on vehicle microprocessors (MCUs) due to their large computational load.

[0065] In terms of skeletal design, the microscopic spatial coordinates are directly eliminated. r Input and The concentration field network branch seamlessly switches the activation function to nn.ReLU(), which is suitable for high-frequency throughput and extremely fast computation speed in MCU hardware pipelines. In knowledge distillation, the trained teacher PINN model is applied to the outermost surface of the particles (…). The smooth voltage residual curve derived from the inverse reasoning is used as a high-value "soft label," while the sensor-measured residual is used as a "hard label." The model is continuously updated during data loading, allowing students to concentrate all their computing power on memorizing the soft labels taught online by the teacher.

[0066] Figure 5 The prediction performance of the RC-ECM benchmark model after incorporating an ANN was demonstrated. After removing the cumbersome microscopic partial differential derivative chain, the time overhead of forward inference across all operating conditions plummeted due to the input dimension dropping from a high-dimensional to a smooth four-dimensional macroscopic space. The runtime of the student small model ANN was reduced by 99%, and the online inference speed increased by 100 times, enabling high-frequency, low-latency real-time online inference on an automotive microcontroller. Furthermore, the final terminal voltage prediction RMSE error was controlled at 5.16 mV. Figure 5 (b) shows that the terminal voltage prediction error (blue curve) of the ANN+RC-ECM combination is significantly smaller than that of the traditional second-order RC-ECM (pink curve).

[0067] (5) ANN-assisted ECM for online closed-loop SOC estimation.

[0068] To comprehensively test the closed-loop control robustness of the proposed ANN and second-order RC-ECM benchmark model fusion framework in a real vehicle deployment environment, this invention conducted an online state of charge (SOC) reconstruction experiment under the complex dynamic cyclic discharge conditions of a CHTC city bus. Considering that actual vehicle management systems are prone to the engineering challenge of unknown initial SOC due to long-term dormancy or transient sensor power outages, this invention artificially introduces an initial SOC fault error of up to 20% at the beginning of the algorithm startup, thereby rigidly verifying the observer's closed-loop feedback convergence speed and correction capability.

[0069] like Figure 6 As shown by the red dashed line, the uncompensated traditional second-order RC-ECM combined with the standard EKF observer exhibits severe limitations. Under the intense stress of high-rate operation with varying temperatures, the traditional circuit model lacks the dynamic capture capability of irreversible nonlinear characteristics such as microscopic solid-phase lithium-ion diffusion distortion and heat transfer balance within the battery cell. This results in a severe spatiotemporal misalignment between the observed voltage space and the actual physical space of the battery. This leads to a significant accumulation of voltage prediction residuals in the traditional framework during operation, making it impossible to provide accurate voltage update values ​​for the Kalman filter. Under the dual pressure of high impedance faults and polarization distortion, the feedback regulation mechanism of the standard EKF becomes passive, unable to accurately identify, track, and correct the 20% initial fault error.

[0070] In stark contrast, the hybrid mechanism observation framework proposed in this invention exhibits near-perfect rigid convergence and state-locking performance. Despite being injected with severe initial biases in the initial stage, the observation equations within the filter seamlessly stitch together the lightweight ANN operator after knowledge distillation, which precisely inherits the smooth physical manifold of the single-particle model (SPM). Figure 6 The blue curve shows that in the early stage of operation, the filter uses a high-precision nonlinear voltage residual patch for closed-loop correction negative feedback, and completes the SOC estimation correction with an extremely high convergence slope in a very short time.

[0071] After entering the physically stable convergence region, the root mean square error (RMSE) of the closed-loop terminal voltage and the absolute error of SOC prediction in the stable segment both showed excellent performance. This strongly demonstrates that the strategy of avoiding the cumbersome PDE automatic differentiation chain of PINN through ANN knowledge distillation not only frees up the computing power of the vehicle-side microcontroller (MCU), but also achieves high-precision and robust battery state reconstruction at the closed-loop control level.

[0072] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A physical constraint mechanism and power battery capacity estimation method without intrinsic parameter dependence, characterized in that, Includes the following steps: Step 1: Based on bench experiments, acquire battery external characteristic data under complex dynamic conditions and different temperature ranges to obtain a mechanism dataset; construct a second-order RC-ECM benchmark model based on the mechanism dataset, and obtain the benchmark macroscopic terminal voltage based on the second-order RC-ECM benchmark model. Step 2: Obtain the macroscopic predicted voltage residual based on the reference macroscopic terminal voltage and the actual measured voltage; Step 3: Construct a physical information neural network, and embed the solid-state diffusion partial differential equation and boundary conditions evolving with temperature in spherical coordinates as physical constraint terms into the loss function of the physical information neural network; take time, current, temperature, and state of charge as inputs, and the macroscopic predicted voltage residual as data supervision term to obtain the nonlinear electrochemical voltage dynamic correction quantity; Step 4: Using the physical information neural network as the teacher network and the nonlinear electrochemical voltage dynamic correction amount as the soft label, train an ultra-lightweight feedforward neural network. Step 5: Deploy the ultra-lightweight feedforward neural network in the vehicle battery management system, and run it synchronously with the second-order RC-ECM benchmark model at the same frequency to continuously output the nonlinear electrochemical voltage dynamic correction amount; The nonlinear electrochemical voltage dynamic correction is input into the measurement equation of the Kalman filter to obtain the battery state of charge estimate.

2. The physical constraint mechanism and power battery capacity estimation method without intrinsic parameter dependence according to claim 1, characterized in that, In step 1, the state-space equations of the second-order RC-ECM reference model are established, and the state-space equations are discretized using the first-order forward Euler method to obtain the state transition equations. Based on the state transition equations, the reference macroscopic terminal voltage is obtained. ； in, ； ； In the formula, express The reference macroscopic terminal voltage at that moment; Indicates open-circuit voltage; express The virtual state of charge at any given moment is calculated by the ampere-hour integral; express k Current at any moment; Indicates the internal resistance of the ohm; Indicates charge transfer impedance; Indicates charge transfer capacitance; Indicates concentration polarization impedance; Indicates concentration polarization capacitance; , They represent k The polarization voltages of the two RC loops at any given time; Indicates the sampling period; , They represent k+ The polarization voltages of the two RC loops at time 1.

3. The physical constraint mechanism and power battery capacity estimation method without intrinsic parameter dependence according to claim 1, characterized in that, The composite multi-objective total loss function of the physical information neural network includes: ； In the formula, Represents the total loss function for composite multi-objectives; Represents the loss function for data-driven terms; This represents the residual loss function of the physical partial differential control equations; Represents the boundary condition residual loss function; These are the weighting coefficients for the data-driven term loss function, the physical partial differential equation residual loss function, and the boundary condition residual loss function, respectively.

4. The physical constraint mechanism and power battery capacity estimation method without intrinsic parameter dependence according to claim 3, characterized in that, The residual loss function of the physical partial differential equations includes: ； In the formula, This indicates the concentration of lithium ions in the solid phase inside the active particles; This represents the solid-phase diffusion coefficient, which is strongly coupled with the real-time operating temperature. Indicates the radial radius position of the microscopic particles; Indicates the runtime.

5. The physical constraint mechanism and power battery capacity estimation method without intrinsic parameter dependence according to claim 1, characterized in that, In step 3, the physical information neural network takes time, current, temperature, and state of charge as inputs to obtain the concentration distribution state; by constructing an electrochemical cross-border translation and voltage fusion layer, the concentration of the outermost surface of the active particles is extracted from the concentration distribution state. and the average concentration inside the active particles Normalization was performed to obtain the surface stoichiometry. and average stoichiometry ;in, The maximum saturated solid concentration is represented by the Butler-Volmer kinetic equation in the charge transfer process and the solid concentration polarization mechanism induced by the surface-to-average concentration difference, to obtain the dynamic correction amount of the nonlinear electrochemical voltage. : ； In the formula, Represents the ideal gas constant; Indicates the operating temperature of the battery surface; Denotes Faraday's constant; This represents the molar flux through the pores on the electrode surface. Indicates the exchange current density; This represents the electrode equilibrium potential function.

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